for the mathematically inclined

square roots

These two photos are of a tree that grows alongside the cycle track that runs parallel to Pak Wo Road in Fanling. The brick paving, which has been laid in a single basket-weave pattern, has constrained the directions in which embryonic roots of the tree near the surface can grow, and all changes of direction are right-angles.

In the bottom left-hand corner of the second photo, the paving changes to a series of parallel stretcher courses, which explains the tight turn of the root nearest the camera through two right-angles.

the first ten thousand

You might think that someone who has lived in Hong Kong, off and on, for almost 50 years would be familiar with all the ‘attractions’ that the territory has to offer. But you would be wrong.

A few weeks ago, we received a notification from the local power company informing us that our electricity would be off between 9am and 3pm on a specified day in the near future. That meant no internet, and no point in staying home while the power was off. Paula suggested a bus ride to Sai Kung, but although the Sai Kung peninsula is one of the most scenic places in Hong Kong, I’d lived in the area between 1974 and 1989 and was therefore very familiar with the entire area. And we’d both lived in the area between 2005 and 2008, when we moved to Fanling. I suggested taking a bus to San Tin, which has quite a few historical buildings, but we’d both visited the place several times.

Then I had a bright idea: why not visit the Ten Thousand Buddhas Monastery in Shatin. I thought I knew precisely where it’s located, because I’d caught a glimpse of a pagoda high on the hillside while passing through Shatin on the train. And that’s where we went for the day.

It took us a while to locate the entrance, but when we did, it was obvious that we’d come to the right place:

The gilded statues are all arhats (arhat is a Sanskrit word meaning ‘one who is worthy’, one who has gained an insight into the nature of existence and has therefore achieved nirvana, spiritual enlightenment, and can thus escape the endless cycle of death and rebirth).

There is only one path, and it’s lined with arhats:

This is a view looking back down the way we’ve just come:

Incidentally, there are 341 steps on this path, although we didn’t find it particularly arduous because I kept stopping to take photos, including from time to time a close-up of some of the arhats:

And still the climb continues:

Another close-up:

You might expect that such statues would be endless repetitions of the same figure, but you will have noticed that each one is different, although whether they’re modelled on real people I’m unable to say.

This is a view looking back down the hill from where I took the previous photo:

And there is still some way to go uphill:

A final look downhill:

…although the climb still continues for some distance:

There is a sharp turn to the left at the top of the steps in the previous photo, and this is a close-up of the figure on the outside of the turn, which you can see in the previous photo:

…and this photo is of the statues to the left of the figure in the previous photo:

Notice the figure on the right with the preternaturally long arm. I don’t know what he’s reaching for.

And this is the final climb:

These are the statues at the top of this incline:

However, when the path levels off, there are more gilded statues:

I don’t know why the figures in the previous photo are female, but they probably represent goddesses.

And then we arrived at a large platform in front of a temple:

The procession of strange figures on the roof of the pavilion are a ubiquitous feature of traditional Chinese buildings: a pilgrim riding what appears to be a donkey; a line of three (you sometimes see four or five) not quite identical mythical beasts; and, finally, someone riding another mythical beast.

I didn’t photograph the white statue in the pavilion, but this is the imposing figure that stands back to back with it:

There is also a nine-storey pagoda on the platform (this is what I could see from the train):

There are other interesting statues around the outer rim of the platform:

I’m unable to say what they mean or who they represent.

And this is the temple:

Note the splendid dragons facing each other on the front. And the bronze tripod, which is there for worshippers to plant burning joss sticks. There are also dragons climbing up each side.

At this point, you may well be wondering about the name of this place. There certainly aren’t 10,000 life-size statues, but there are thousands of tiny gilded buddhas set into niches in the internal walls of the temple. Unfortunately, there are signs expressly forbidding any photography inside any of the buildings, so all I can say is that the cavernous interior is extremely impressive.

There is a short climb to the right from the end of the long climb that brought us here:

And this is the view from the top, looking down:

…while this is close-up of the figures on the outside of the bend:

There is another temple here:

…but the most impressive sight here is the rectangular ‘courtyard’ surrounded on three sides by stone statues:

The previous photo shows part of a design set into this paved area, and this is what the full design looks like:

It features a monad in the centre and the twelve animals of the Chinese zodiac around the outside. Starting with the nearest one in the photo and moving clockwise, these are rabbit, dragon, snake, horse, goat, monkey, chicken, dog, pig, rat, ox and tiger.

This is a closer view of the ten statues at the end of the ‘courtyard’ and what appears to be a tiger in the left-hand corner:

…while this is a closer look at the figures on the right, as viewed from the end of the ‘courtyard’:

There is a stone dragon at the far end in the second photo.

Here are some of the figures on the opposite side:

And there is a goddess with eight arms halfway along the row:

It was only when I examined the photos after I got home that I realized there is an inscription below each statue. I’d categorized the statues as being either warriors, scholars or court officials, but now I wonder whether each one represents a real historical person (they are all male). The inscription under the statue on the left indicates that this is Lo Ching, who, according to the inscription, was ‘a great general’.

There is a smaller temple to the right of the previous one (photographed above):

All the temples here have imposing statues 6–7 metres high inside, on each side of the entrance, and the figure on the left in this temple is actually mounted on a horse and wielding a halberd. As I’ve already mentioned, photography inside the temples is not allowed, so you would need to see these figures for yourself.

To the right of the previous photo is a makeshift fence. According to a leaflet that Paula picked up, there was a landslide here in 1997, probably due to inadequate slope maintenance, and access to a higher level that houses four more temples is currently not possible.

This view of the larger temple, taken from in front of the smaller temple, shows the two dragons on the roof ridge, a common feature on temples here in Hong Kong:

We’d now seen everything that we could see, and it was time to leave. We could have gone back down the way we’d just come up, but we’d noticed steps leading down from the front of the platform I referred to earlier. It seemed prudent to ask someone who was employed by the monastery whether the steps led back down to the valley floor, because I didn’t fancy having to come back up if this exit route was blocked. These steps are much steeper than the ones we’d come up earlier.

There isn’t much to see on this descent route. Just two statues, far apart:

I’m glad we didn’t accidentally find this way up, partly because it’s so steep but also because the lines of gilded statues would not have seemed so impressive on the way down. Finally, I should point out that this is not an historical site. According to the leaflet that I referred to earlier, construction didn’t begin until 1951. But this is still a great place to visit and will be on the itinerary for any guests we have in the future.

the domain of the tiger

In January this year, I walked downstream along our local river to check out the most spectacular example of a firecracker vine that I’d ever seen, in the village of Fu Tei Au. It didn’t disappoint, but I also discovered an impressive mural with a new year theme and the record, on a stone tablet, of a catastrophic flood that had occurred in 1972, before the river was canalized.

I wanted to show Paula what I’d found, so a few days later we visited the area, and it was Paula who spotted the sign that pointed up a narrow alleyway to a ‘seven colours ancient well’. I wrote about all this in An Educational Excursion.

A few weeks later, we just happened to be walking along Fu Tei Au Road when I noticed some admittedly corny artwork on a building on the south side of the road:

A very short distance further on, this is what we saw:

It appeared to be some kind of museum that reflects the history of the village, but we were unable to go in to take a closer look:

Presumably it was closed because of pandemic restrictions.

However, last month I thought that it might be worth checking to see whether it was now open. And it was:

This photo was taken from inside the gate, and you can see more artwork to the left of the building adorned by the ‘tiger’. Incidentally, ‘Fu Tei’ means ‘domain of the tiger’, and the name relates to a tiger that was killed in the area in 1915 (the last tiger in Hong Kong wasn’t killed until the mid-1920s). Hence the ‘tiger’ painting on the building.

In my earlier report, I expressed surprise that the collection of houses in the vicinity of the ‘colourful well’ were designated a village, because there were no houses built under the terms of the so-called small house policy introduced by the British administration in 1972. However, this village was established by refugees from the Chinese civil war, which ended in 1949, and the small house policy applied only to villagers who could trace their ancestry to a male in their village before 1898, when the British took over the New Territories. I also cited the absence of a public toilet, but I’ve since discovered that the Fu Tei Au Public Toilet is located on the north side of the junction between Fu Tei Au Road and Man Kam To Road. In fact, the entire area circumscribed by Fu Tei Au Road, Man Kam To Road and the Ng Tung River appears to be part of Fu Tei Au.

The ’tiger building’ houses a small museum that details the history of the domain of the tiger, and among other things I learned, the Lo Wu Brick Company obtained leases to parts of this area in 1921, and its workers dug the ‘colourful well’ to ensure a supply of potable water. The well was lined with concrete made from locally sourced, brightly coloured gravel, hence the name, although no sign of this colour now exists, which is why, in my earlier report, I’d conjectured that the colour was due to sunlight being refracted by water vapour.

What follows are some of the highlights of the museum, starting with these photographs:

Clockwise from the top left, the titles read ‘Pond of Flower Field’; ‘Habitat of Egrets’; ‘Habitat of Fireflies’; and ‘Ng Tung River’.

These photos reflect the cultural life of the village:

And these models are of features of interest:

The ‘stilt house’ can still be seen, but I don’t think the ‘ponds house’ exists now.

However, it is the artwork on the various huts that I found especially interesting. I didn’t write up an account of this fascinating location after our earlier visit, because I neglected to take a photo of the hut in the next photo, first because there were other visitors, and I couldn’t get a clear shot, then, when we were leaving, I convinced myself that I’d already taken a photo of it. We went back yesterday, and I took this photo:

I included a photo of the miniature brick-arch bridge in An Educational Excursion, and the ponds on each side are still filled with water hyacinths, although you would be extremely lucky to see them flowering. The bird depicted on the right is a red-crowned crane, although I’ve never seen this species in this area. There are egrets flying overhead.

There are more birds on the wall of the building to the right:

Incidentally, the ornaments hanging down are soft-drink cans that have been slit vertically multiple times. I saw the same decorations when I first visited ghost alley.

This is the building to the left:

This is actually a bathroom. Yes! It does have a bath in addition to a toilet bowl. I know because I had to use it yesterday. I don’t think that any of the butterfly images represent any of the more than 200 species that have been recorded in Hong Kong.

And this is the left-hand side of the first building:

The brickwork continues around the corner:

…and this is the fourth side of the building:

…while this is the side of the ‘butterfly bathroom’:

If you walk through the gap seen in the last photo and look left, this is what you will see:

This is also a bathroom (I know because I had to close the door in order to take the photo).

And this is the view straight ahead:

To the right of the building in the previous photo is a building comparable in size to the ‘tiger building’, and it is adorned with perhaps the most detailed artwork here:

The flowers are lotus, and there are kingfishers on the left.

The inscription relates that when wind and rain come at the right time, the harvest is optimized. The mountain in the background is Peach Blossom Mountain (peaches are a symbol of longevity in Chinese culture).

Directly opposite the artwork in the previous two photos is a canvas suspended high above the ground:

This is a general view of the open area that I’ve just walked through:

Meanwhile, there is more artwork on the large building around the corner to the right:

…and a large well:

The inscription advises you to know the source of your water. I don’t know whether this is a real well or yet another piece of artwork.

The building to the right of the one with the first artwork I featured above has a small room (on the right) filled with artefacts from a bygone age:

Exhibits include a sit-up-and-beg bicycle, a treadle-operated sewing machine, a cathode ray tube television and, on the far wall, a range of primitive farming implements:

It was only when I looked at the photos that I realized that each exhibit had a label, presumably explaining what each exhibit represents.

This painting is on the opposite wall to that with the tiger (above):

The child on the right is praying for peace, happiness and prosperity. His prayer appears to have been answered.

As you enter this site, there is a line of wooden pallets on the left with artwork painted on them. While I’d been walking around, Paula had engaged in a long conversation with a young man from the Chinese University of Hong Kong (ChineseU) who was working on the site. She learned that although the artwork on the buildings was done using commercial paints, that on the pallets had been done using traditional pigments, so they have faded quite badly. I’ve therefore included just one photo of this work:

In fact, I believe that all the artwork here was done by ChineseU students, and during the course of her conversation, Paula learned that architecture students from the university had planned to develop an ‘eco-park’ in the area, but funding for the project will end in February next year, and so, presumably will the project.

As we were leaving, I noticed this confrontation between a pig and a rooster from the road:

It wasn’t there when we visited last month.

Finally, here are two maps of the area. I photographed the first in the ‘tiger building’, and the second is a more conventional map:

The red circle indicates the approximate location of the ‘colourful well’, while the blue circle shows the location of this fascinating site. I can’t say that it’s unique, but it’s certainly unusual.